Volume 9, no. 4Pages 53 - 62

# On Application of the Structure of the Nonlinear Equations System, Describing Hydraulic Circuits of Power Plants, in Computations

A.A. Levin, V.F.Chistyakov, E.A. Tairov
This paper presents the results of applying the methods of the hydraulic circuit theory in the interactive modeling of hydrogasdynamic and thermal processes that occur in the equipment of thermal power plants. The problem statement of flow distribution in the energy plants with different pressure drop laws in the branches of complex gas air and steam-water ducts is formulated. The research shows that the application of traditional methods of hydraulic circuit theory is challenging for such problems. Some aspects of solvability of the related systems of nonlinear equations are studied. The numerical methods for solving these systems as applied to the problems that require calculations in real time are considered. A computation scheme is proposed. The scheme makes it possible to reduce the initial statement of the problem to the classical scheme of the nodal pressure method. The method of decomposition of the hydraulic circuit configuration into interconnected circuits of smaller dimension is considered to reduce the computational effort. The results of tests that demonstrate high reliability of the method developed for the flow distribution calculation are presented.
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Keywords
hydraulic circuits; mathematical models; ducts of power plants; systems of nonlinear equations; Newton method; fixed point iteration method.
References
1. Merenkov A.P. Hasilev V.Ya. Teoriya gidravlicheskikh tsepey [Theory of Hydraulic Circuits]. Moscow, Nauka, 1985. 278 p.
2. Shashkov O.K., Shashkov V.O. [Calculation of the Variable Mode for the Heat and Power Plants with Steam Turbines Using the Hydraulic Circuits Method]. Teploenergetika [Thermal Engineering], 2004, no. 4, pp. 67-71. (in Russian)
3. Levin A.A., Tairov A.E., Chistyakov V.F. [Load Flow Analysis in Power Supply Plants as in Hydraulic Circuits with Controlled Parameters]. Truboprovodnye sistemy energetiki: matematicheskoe modelirovanie i optimizaciya [Pipe System of Power Industry: Mathematical Modelling and Optimization], Novosibirsk, Nauka, 2010, pp. 115-124. (in Russian)
4. Peterson D.F., Saminskaya L.V., Khabenskiy V.B. [On the Subject of Hydraulic Calculation for the Straight Through Subscritical Boiler on the Electronic Digital Computer]. Trudy Tsentral'nogo kotloturbinnogo instituta [Bulletin of the Central Boiler-and-Turbine Institute], 1969, issue 98, pp. 60-70. (in Russian)
5. Vul'man F.A., Khor'kov N.S. Teplovye raschety na ECVM teploehnergeticheskikh ustanovok [Thermal Calculation of Heat and Power Plants on the Electronic Digital Computer]. Moscow, Energiya, 1975. 200 p.
6. Ivanov V.A. Rezhimy moshchnykh paroturbinnykh ustanovok [Operation of Large Steam-Turbine Plants]. Moscow, Energiya, 1971. 280 p.
7. Raschet i proektirovanie pyleprigotovitel'nykh ustanovok kotel'nykh agregatov [Analysis and Engineering for Fuel Pulverizing Plants of Boiler Units]. Leningrad, Tsentral'nyiy kotloturbinnyiy institut, 1971. 310 p.
8. Krasnoselsky M.A., Vainikko G.M., Zabreiko P.P. et al. Priblizhennoe reshenie operatornykh uravneniy [Approximate Solution of Operator Equations]. Moscow, Nauka, 1669. 456 p.